What is political traditionalism?
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Broadly speaking, it's simply an espousal of traditional political principles rather than the espousal of relatively modern, liberal political principles. As the article suggests, the Western left and right are two different flavors of liberalism.
But what are traditional political principles? Or, do you have a link for me to figure this out? 
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I'm not sure that it can be summed up in one work or one site. Boiled down to its most common principles however, I would say that it is:
1) Virtue and truth based rather than autonomy or "freedom" based.
2) Accordingly, it recognizes that legislation must reflect the moral needs of the people; laws provide a medicinal and educational purpose. Laws do not exist simply to litigate power struggles between citizens or corporations.
3) The political and communal aspect of man is constitutive of his nature as a rational animal. Man is inherently political and social. As such, the society must be treated not just as a collection of individuals, but also as a living entity itself, a whole composed of smaller parts. The smallest and most fundamental cell of society is the family. The State is analogous to the family, and works in a similar manner as it is simply the family writ large.
4) Egalitarianism is rejected for hierarchical forms of governance. The desire and need for hierarchy is constitutive of the human experience. It also provides the basis for real subsidiarity, as all members within the society have their own place. Responsibilities are easily adjudicated, which is often not the case in democratic or representative forms of government.
5) Politics are teleological. The aim is the flourishing of the citizens. At the very least, this involves ordering the society toward the virtue of its citizens, toward their natural end. Ideally, it also aims to aid citizens toward the achieving of their supernatural end of beatitude. This is primarily the responsibility of the Church, but the State acts as Her handmaiden. Insofar as temporal affairs affect our spiritual life, the State is charged with aiding the Church in the attainment of that end.
6) A traditional society does not solve all moral issues via economics and the financial market. It recognizes that issues of social justice are not simply private. Since these injustices regard temporal goods and public suffering, the State has a very formal place in addressing and rectifying them.
7) There is a distinction but no functional divorce between the Church and the State. As many modern political commentators have written, it is impossible for the Church and the State to remain completely separated. The current state of the West is an example of how such a separation invariably leads to the subjection of the Church to the State. The traditional response is to restore the State's submission to the Church.
8 ) This leads to the rejection of the compartmentalization of faith. The State confesses a religion as true, rather than espousing a religious and philosophical plurality. A State or culture which does not share common values and beliefs cannot stand together.
I would say that this is a good start.
